Dear Editor


We acknowledge that both referees do not find the manuscript suitable for publication in PRL because they consider the reported experiment not sufficiently relevant for it.
At the same time, the referees acknowledge the scientific correctness of our report.
We have addressed the point indicated by the referees and we believe that the modified text better express the relevance of out work and we would be glad if you could consider the manuscript for publishing in PRA.


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Reply to the Referee A


1) In the manuscript we acknowledge that the exponential shape of the waveform, per se, it is not surprising:
	"This can be easily understood by the timing sequence of a cascade decay, where the signal photon heralds the population of the intermediate level, which subsequently decays exponentially, leading to the characteristic decaying envelope of the idler photon according to the Weisskopf-Wigner solution [23, 24]"

On the other hand we stress the rising nature of the exponential envelope of the signal photon when heralded by the detection of the idler photon.
This type of temporal envelope has not been observed very often in the past decades and has instead been sought for its predicted properties of enhanced interaction with a two level system ( see ref ).


2) We agree with the Referee that cross correlation experiment lead to asymmetric shapes.
This is why we extended our experimental investigation beyond the measurement of the cross correlation to the measurement of the field envelope using optical homodyning technique: not looking for surprises but to confirm what the cross correlation measurement suggested.

3) We thanks the Referee to rise this point. In a previous work [16] we have already addressed in a quantitative way the effect of the atomic density on the bandwidth of the generated photon pairs.
We modified the text of the manuscript in order to make explicit that for a quantitative analysis of the correlation between the photon bandwidth and the optical density of the atom cloud the interested reader can refer to our previous work.

The paragraph that in the original manuscript read:
	"The time constants for the exponential rise or fall times are compatible with the distribution of detection time differences we observe in the cascade decay [16], enhanced by the dense atomic ensemble [26]"

now reads:
	"The time constants for the exponential rise and decay profiles are shorter than the lifetime of the intermediate state. This is due to collective decay effects observed in dense atomic ensembles [25]. The measured value is compatible with our previous measurements of the distribution of detection time differences for this optical density [15]." 

4) We agree with the Referee that the observed photons present a larger bandwidth than the natural linewidth of the atomic transition of interest. While in this manuscript we do not directly interact the generated photons with an atomic system, we do not consider the bandwidth a fundamental limit.
As indicated in reply to point 3), the bandwidth of the generated photons depends on the optical density of the atomic cloud, a parameter we can control, as demonstrated in our previous work.


5) We agree with the Referee that in order to observe an interaction between the generated photons and an atomic system the photon need to be resonant to a ground state transition of the atom.
We modified the text of the manuscript to state explicitly that the photon with exponentially rising waveform is not directly suitable for interacting with an atom in free space.
We also indicate how the temporal correlation of the generated photons combined with a recently time shaping technique, named time reversal by its authors [Bader, et al., New Journal of Physics 15, 123008 (2013)] can be used to generated photons with the desired time shape and resonant with a ground state transition.

The first paragraph of the manuscript was changed from:
	"Strong atom-light interaction at the single quantum level is a prerequisite for many quantum communication pump and computation protocols [1–4]. In free space the optimal coupling of photons to atoms requires the temporal profile of the incoming photons to match the time reversal of photons generated by spontaneous decay from the transition of interest. [5–7]."
to:
	"Strong interaction in free space between a single photon and a two-level quantum system is a prequisite for many quantum communication and computation protocols [1–4]. This interaction has been demonstrated to be optimal when the incident photon has an exponential rising temporal envelope [5–8]."

The conclusion of the manuscript has been modified also. From:
	"If heralded single photons are practically not distinguishable from "true" single photons, the latter should — at least in principle — efficiently be absorbed by a single atom in free-space in a time-reversed Weisskopf-Wigner situation. Such an experiment would therefore not only demonstrate strong atom-photon interactions, but also provide a better understanding to what extent heralded photons are equivalent to single photons emerging from a setup with a well-defined initial condition."
to:
	"If heralded single photons are practically not distinguishable from "true" single photons, the latter should at least in principle be efficiently absorbed by a two-level system in free-space in a time-reversed Weisskopf-Wigner situation. Such an experiment also would provide a better understanding to what extent heralded photons are equivalent to single photons emerging from a setup with a well-defined initial condition. This test would require a photon driving a ground state transition of a two level system. The heralded photons with the exponentially rising waveform generated by our scheme are resonant with an excited transition and there- fore cannot be used directly. However, waveform reshaping techniques demonstrated in [8] can be employed to address this problem."


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Reply to Referee B


1) We agree with the Referee that the homodyne method is indeed not new and, as such, it is also well known the difference between measuring the correlation between two fields, as presented in Ref.6,  and the envelope of a field, as presented in the manuscript.

2) After reading carefully the insightful comment of the Referee we removed the world counterintuitive from the title of the manuscript. 
We still believe that the experimental measurement of a rising exponential is relevant in the context of modern quantum optics.
The correlation measurement presented in our previous work [ref. 6] clearly hinted at the presence of two symmetrical temporal waveform, presence that we decided to confirm by experimentally measuring the temporal shape of the individual photons.

3) We are aware of the works of Harris group (cited in the original manuscript). We are also aware of Du's group efforts, based on the original works of Harris.
We claim that our approach as an inherently distinguishing prerogative: the temporal shape of the photons is governed only by the dynamics of the cascade process. This rises also interesting questions regarding the reality of the heralding process as state preparation, described in the conclusion of the manuscript.
We added the following text to the introduction of the manuscript to clarify the difference between the approach used previous works cited by the Referee:

In the introduction, the text was modified from:
	"Single 87Rb photons with an exponentially rising temporal envelope have been prepared from such a heralded single photon source by direct modulation of one of the photons of the pair [14]."
to:
	"Heralding has already been used to generate single photons with rising exponential temporal envelopes: the intensity of one photon of the pair is modulated in time using fast modulators [12, 13].
	This modulation technique resulted in unavoidable losses due to the small overlap between the temporal shape of the generated photons (exponential decay) and the desired one (exponential rise)."

4) We thank the Referee for noticing an error in the transcription of the normalization formula. The correct formula, that now appears in the revised manuscript, is the one used to obtain the plots in fig. 2.
Regarding the reference to Aspect's work: in their work the authors did not take into account the use of coincidence time windows of different duration.
In our work we sample the arrival of the detection events with a resolution of 125ps. This allow us to observe the correlation as function of the difference in arrival time for the Hanbury Brown Twiss interferometer.
In order to properly normalize the correlation we had to devise a more complete normalization function to take into account both the sampling of the delay between the two arms of the interferometer and the time window opened by the heralding event.
We have verified that our normalization reduces to Aspect et al. one when we take a unique coincidence window for the threefold coincidence events.
We would also like to stress how all the values used in the normalization and in the derivation of the g(2) are measured.

In equations (2) and (3) the factor 1/Ns has been added and in the text just before the equation the following sentence has been added:
	"[...] normalized to the total number of triggers Ns."